# Sum of Three Values

## Problem Statement

Given an array of integers and a value, determine if there are any three integers in the array whose sum equals the given value.

Consider this array and the target sums.  ## Hint

• Sort data
• Iterate from both ends

## Try it yourself

bool find_sum_of_three(vector<int> arr,
int required_sum) {
// TODO: Write - Your - Code

return false;
}

## Solution

bool find_sum_of_two(vector<int>& A, int val,
size_t start_index) {
for (int i = start_index, j = A.size() - 1; i < j;) {
int sum = A[i] + A[j];
if (sum == val) {
return true;
}

if (sum < val) {
++i;
} else {
--j;
}
}

return false;
}

bool find_sum_of_three_v3(vector<int> arr,
int required_sum) {

std::sort(arr.begin(), arr.end());

for (int i = 0; i < arr.size() - 2; ++i) {
int remaining_sum = required_sum - arr[i];
if (find_sum_of_two(arr, remaining_sum, i + 1)) {
return true;
}
}

return false;
}

int main(){
vector<int> arr = {-25, -10, -7, -3, 2, 4, 8, 10};

cout<<"-8: " <<find_sum_of_three_v3(arr, -8)<<endl;
cout<<"-25: "<<find_sum_of_three_v3(arr, -25)<<endl;
cout<<"0: " <<find_sum_of_three_v3(arr, 0)<<endl;
cout<<"-42: " <<find_sum_of_three_v3(arr, -42)<<endl;
cout<<"22: " <<find_sum_of_three_v3(arr, 22)<<endl;
cout<<"-7: " <<find_sum_of_three_v3(arr, -7)<<endl;
cout<<"-3: " <<find_sum_of_three_v3(arr, -3)<<endl;
cout<<"2: " <<find_sum_of_three_v3(arr, 2)<<endl;
cout<<"4: " <<find_sum_of_three_v3(arr, 4)<<endl;
cout<<"8: " <<find_sum_of_three_v3(arr, 8)<<endl;
cout<<"7: " <<find_sum_of_three_v3(arr, 7)<<endl;
cout<<"1: " <<find_sum_of_three_v3(arr, 1)<<endl;

return 0;
}

## Solution Explanation

Constant, O(1)

### Solution Breakdown

In this solution, we first sort the array. Then we fix one element ‘e’, and try to find a pair (a, b) in the remaining array such that required_sum - e = a + b.

We start with the first element e in the array (at index i = 0) and try to find such a pair (a, b) in the remaining array (i.e A[i + 1] to A[n - 1]) that satisfies the condition: a+b = required_sum - e. We can find such a pair in linear time. If we find such a pair, we have found the solution: a, b and e and thus, we can stop the iteration.

Otherwise, we repeat the above steps for all elements e at index i = 1 to n - 3, until we find a pair that meets the condition.

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